In economics, there are no heroes. Let's repeat that: there are no heroes.

We want heroes. We want to be told what is right by philosopher-data-kings, poring over numbers that will point us toward the right policies and ways of thinking. When we want to address inequality – like raising the minimum wage or paying women an equal amount, or giving immigrants a chance to contribute to society, or paying CEOs less – economics helps bolster those arguments. To a certain extent, the numbers created by the magi of the economy have been our beacons through the recession and the slow recovery. We look to the wise men (and women, but mostly men) who will lead us out of the wilderness, their white robes printed with numbers: GDP, unemployment, inflation. These numbers are our mile markers: how much is life improving for people? Can they afford food? How much further does the economy have to go to recovery?

We are, largely, fools when we do this. Economics is an inexact science, as any honest economist will tell you. It is based on unreliable numbers that measure relatively small swaths of the population. Whatever the number – unemployment, inflation, wages – it is almost always wrong the first time the government publishes them, and then it is revised later: once, twice, three times or more. The errors are usually large.

This is an important realization because of what happened this week. Many Americans know that Washington lawmakers have been engaged in a two-year battle to the death over the federal deficit. Some, like Congressman Paul Ryan, say that the debt that America owes will destroy the economy in the future. Others, mostly Democrats, say it is foolish to cut government debt – and thus government spending – because Americans need the wages and support that come from Washington, at least until things get better.

This philosophical debate is not actually about philosophy. It has been, to a certain extent, about two activist economists who spent years preaching that high debt would destroy America's economy in the future, pitching us into certain recession. Here's how it happened:

In 2011 Congress was engaged in a bitter battle over the direction of the US economy; a group of them seemed ready to default on the nation's debt and shut down the government, if necessary, to win their point: that the growing federal deficit would endanger America's economy for generations to come. Others were unconvinced. The stalemate brought Washington to a standstill on the issue.

During this tense period, there was an important meeting. Nearly 40 Senators sat in neat rows to hear a presentation on debt from Carmen Reinhart and Ken Rogoff, two economists with faultless reputations and keen academic credentials. They were not just economists that day, however, bolstered by years of research and a 900-pound book full of graphs and complex economic data, Reinhart and Rogoff were also activists against debt. Their goal was to convince the assembled lawmakers to cut the amount of money the government owed.

The data from Reinhart and Rogoff showed that if the national debt became equivalent to 90% of the US gross domestic product, the US would suffer low growth and all that comes with it: unemployment, malaise, poverty. Reinhart and Rogoff had faultless authority; in 2009, they had published a 900-page doorstopper of a book full of graphs and charts dryly titled This Time It's Different.

Reinhart and Rogoff wrote in the introduction:

"What is certainly clear is that again and again, countries, banks, individuals, and firms take on ex­cessive debt in good times without enough awareness of the risks that will follow when the inevitable recession hits. The fact that basic data on domestic debt are so opaque and dif­ficult to obtain is proof that governments will go to great lengths to hide their books when things are going wrong, just as financial insti­tutions have done in the contemporary financial crisis.

We hope that the weight of evidence in this book will give future policy makers and investors a bit more pause before next they declare, 'This time is different.' It almost never is."

That anti-debt message was what occasioned their trip to Washington. Rogoff and Reinhart were there to encourage the lawmakers to cut the deficit at any cost, including severe government downsizing. The implication of their presentation was clear: if you think this economy is bad, if you're already hearing from your jobless constituents, wait until you've been suffering through it for 10 more years or more. One can picture the thought bubbles above the senators' heads: they could likely not help but be concerned about their ability to make the right decisions about the economy and hold office if they didn't cut debt.

Rogoff and Reinhart were not there to just present their conclusions; they were there to lobby for them. Senator Tom Coburn, a Republican from Oklahoma, who was there, described the scene and the conversation:

"A key conclusion of [Rogoff and Reinhart's work] is that economies like ours slow down considerably when our debt-to-GDP ratio reaches about 90% (we are now at debt-to-GDP ratio of 100%).Johnny Isakson, a Republican from Georgia and always a gentleman, stood up to ask his question: 'Do we need to act this year? Is it better to act quickly?'

'Absolutely,' Rogoff said. 'Not acting moves the risk closer,' he explained, because every year of not acting adds another year of debt accumulation. 'You have very few levers at this point," he warned us.'"

Even the skeptical lawmakers couldn't help but take this warning seriously, Coburn indicated. Their moods shifted, indicating deep worry, as Coburn tells it:

"'Thank you for your depressing presentation,' Senator Dick Durbin, D-Ill., said in closing, to self-conscious laughter around the room."

Coburn himself was so convinced that he became a leader of the anti-debt movement in Congress. He wrote a book titled The Debt Bomb: A Bold Plan to Stop Washington from Bankrupting America.

This week, here's what we found out: that very convincing data that Reinhart and Rogoff presented was wrong. Their research was messily done with spreadsheet errors. Here's the gist: Reinhart and Rogoff said that economies with more than 90% debt have economic growth of -.1%, which would put them at risk of recessions.

The travails of Rogoff and Reinhart show one thing conclusively: we put too much trust in economics to tell us how to run the country. Economics cannot actually bear this burden. It is largely a science of educated guesses. Economics is a useful science, but it is not an infallible one. It is, in particular, an unreliable policy tool.

There are a few examples.

Let's take employment numbers, for instance. They measure a nation of 300 million people, the government surveys 60,000 households, or 110,000 people. Even then, there's a high chance of being wrong, so the government reserves to be wrong by 100,000 jobs – or nearly the entire size of the group they're sampling.

How about inflation or cost of living? It's measured with the Consumer Price Index, or CPI. First of all, the government isn't measuring how much people in rural areas are paying for food. It measures the costs of food and other goods only for people who are consumers or workers in cities. And the government doesn't ask 300 million people; it asks only 7,000 families to keep diaries about how much they're spending on a basket of 200 products; the diaries lasted for either two weeks or three months.

This is no secret to economists, including the head economist of the United States, Federal Reserve chairman Ben Bernanke. For four years while Congress did almost nothing about unemployment, Bernanke and his colleagues have been coming up with new, innovative ways to stimulate the US economy. The Federal Reserve did things it had never done before: it lent money directly to certain kinds of banks, it increased access to cheap loans when banks wouldn't lend to each other, and it bought billions of dollars in Treasury bonds and mortgage-backed securities to take them off the market so banks would buy other kinds of bonds.

How does the Fed, which has an encyclopedic command of every kind of economic indicator, know all of this is working?

Spoiler: it doesn't.

Bernanke has repeatedly said in press conferences that he believes this stimulus – known as quantitative easing – is working, but also implied that is hard to measure whether the Fed's stimulus moves are making enough of a difference in major economic indicators. In his last press conference, he kept his plans on stimulus open-ended: "to this point we've not been able to give quantitative thresholds for the asset purchases. As we make progress … we may adjust the flow rate of our purchases month-to-month."

Bernanke has spoken of temporary improvements in economic data like jobs numbers. He knows the data can be rocky, and can be misleading if you don't look at it over a long enough time. This even-handedness is probably why Bernanke doesn't get quoted very often in congressional speeches the way that Rogoff and Reinhart have been. Bernanke – as close to a philosopher-king as we have in this country – doesn't want that title, and doesn't try to proselytize. He seems to know that economics has its flaws, and that no single number will tell him whether he was right or wrong to make the policy moves he did. The numbers and research are guides, but they don't settle any debates.

This is the way that economics should be approached: as a helpful supplement to policy, not its entire basis. Economics is called a science, but it's really more of an art. Its numbers are estimates, arguments, and easily debated or disproved.

So the next time that lawmakers point to a single economic study to make their point, be skeptical. The fact that economics spits out cold, hard numbers should not fool us that it produces the cold, hard truth.